A laser-beam machine which can operate as a cutter or trimmer can comprise a CO.sub.2 laser producing the laser beam and a beam guiding and reorienting means to properly direct the laser beam to the workpiece to be processed, for example, to be cut or trimmed.
In cutting a spatially irregular workpiece it is necessary to direct the laser radiation continuously perpendicularly on the position and/or surface to be acted on. In practice this means that troublesome and expensive mechanisms and/or electronic control devices must be provided.